Problem: Simplify the following expression: $z = \dfrac{5k^2 - 50k + 45}{k - 9} $
Explanation: First factor the polynomial in the numerator. We notice that all the terms in the numerator have a common factor of $5$ , so we can rewrite the expression: $ z =\dfrac{5(k^2 - 10k + 9)}{k - 9} $ Then we factor the remaining polynomial: $k^2 {-10}k + {9} $ ${-9} {-1} = {-10}$ ${-9} \times {-1} = {9}$ $ (k {-9}) (k {-1}) $ This gives us a factored expression: $\dfrac{5(k {-9}) (k {-1})}{k - 9}$ We can divide the numerator and denominator by $(k + 9)$ on condition that $k \neq 9$ Therefore $z = 5(k - 1); k \neq 9$